可旋轉式小動物正子斷層掃描系統之影像重建

小動物正子斷層掃描系統為近期經常被使用之PET系統，因醫學相關之研究均須經過動物實驗作為是否能用於人類之依據之一，故本研究使用小動物環形PET系統。醫學臨床上多使用濾波反投影作為影像重建之解析式重建法，但重建之影像品質較差，而疊代式重建法之優點為能夠引入解析式重建法之物理因素，使影像品質更好。本研究使用了MATLAB繪製無雜訊假影以確認重建演算法正確，並透過OpenGATE模擬真實環形PET系統，期望重建之影像能與真實影像接近。重建演算法之系統矩陣使用射束追蹤法計算光子經過互毀效應被偵檢器接收到之路徑長。共軛梯度法(CG)為一般常見之求解最小平方誤差之最佳化演算法，但由於其需計算系統矩陣之轉置矩陣，當重建之系統過大時會使計算時間增加並增加運算複雜度，Chambolle與Pock提出使用原始-對偶最佳化演算法之CP演算法，也能夠求解最小平方誤差，其優勢為計算簡易。而結果雖然CG收斂速度較CP迅速，但隨著疊代次數增加，雜訊也隨之增加。並將CP結合總變異最小化，將影像邊緣保留與降低雜訊，並且透過方均根誤差、條件原始-對偶間距判斷影像品質與收斂程度。並提出可旋轉式稀疏掃描系統，期望能重建出與完整掃描系統相似之影像。

關鍵字

正子斷層掃描；共軛梯度法；原始-對偶演算法；總變異最小化

並列摘要

The small animal ring PET system is frequently used nowadays. Medical-related studies are subject to animal experiments as a basis for the use on humans. Clinical reconstruction often use the filter back-projection as the image reconstruction method. But due to the worse image quality, the iterative reconstruction method can perform better than the analytic reconstruction because it can introduce the physical factors during the reconstruction. In this study, we simulate the noise-free data using the MATLAB to check our algorithm implementation. In addition to use digital phantom, we also used OpenGATE to simulate the real ring PET system. Furthermore, we used ray tracing to calculate photon traveling path to build system matrix. Conjugate gradient and Chambolle and Pock are optimization algorithms for solving the least squares problem. The advantage of CP algorithm is simple to implementation. The result show that although the convergence rate of CG is faster than that of CP, but the noise is getting larger. On the other hand, CP have a simple way to combine to the total variance penalty term in order to preserve the edge. Moreover, we incorporated the normalized mean square error and cPD to check the convergence. At last, we compare image quality of the full scan and sparse scan system.

並列關鍵字

PET ； Conjugate Gradient ； Chambolle Pock algorithm ； Total Variance

參考文獻

Hestenes, M. R., & Stiefel, E. (1952). Methods of conjugate gradients for solving linear systems (Vol. 49): NBS.

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Formiconi, A., Pupi, A., & Passeri, A. (1989). Compensation of spatial system response in SPECT with conjugate gradient reconstruction technique. Physics in medicine and biology, 34(1), 69.

國際替代計量

可旋轉式小動物正子斷層掃描系統之影像重建

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